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An optimal artificial neural network system for designing knit stretch fabrics a
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Hamza Alibi , Faten Fayala , Naoufel Bhouri , Abdelmajid Jemni & Xianyi Zeng a
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LESTE, ENIM, University of Monastir, Monastir, Tunisia
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GEMTEX, ENSAIT, Roubaix, France Version of record first published: 15 Jan 2013.
To cite this article: Hamza Alibi , Faten Fayala , Naoufel Bhouri , Abdelmajid Jemni & Xianyi Zeng (2013): An optimal artificial neural network system for designing knit stretch fabrics, Journal of The Textile Institute, DOI:10.1080/00405000.2012.756134 To link to this article: http://dx.doi.org/10.1080/00405000.2012.756134
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The Journal of The Textile Institute, 2013 http://dx.doi.org/10.1080/00405000.2012.756134
An optimal artificial neural network system for designing knit stretch fabrics Hamza Alibia*, Faten Fayalaa, Naoufel Bhouria, Abdelmajid Jemnia and Xianyi Zengb a
LESTE, ENIM, University of Monastir, Monastir, Tunisia; bGEMTEX, ENSAIT, Roubaix, France
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(Received 26 June 2012; final version received 3 December 2012) In this paper, a computer-aided system for designing knit stretch materials is presented. It allows designers to optimize the structure of knit stretch materials according to the functional properties. This system aims at modeling the relation between functional properties (outputs) and structural parameters (inputs) of knitted fabrics. Thirteen features characterizing knit structures and operating parameters were taken as input parameters of the artificial neural networks (ANNs). These parameters were preselected according to their possible influence on the outputs which were the elongation, growth, and elastic recovery. In order to reduce the complexity of the models, an original fuzzy logic-based method was proposed to select the most relevant parameters which were taken as input variables of the ANNs. The selection procedure of structural parameters allows designers to focus on the most relevant parameters in order to conduct production experiments related to the new product. Then, two types of model are set up by utilizing multilayer feed forward neural networks, which take into account the generality and the specificity of the product families, respectively. The presented models have been validated with the use of experimental data concerning several families of knitted fabrics. Keywords: comfort-stretch; knit fabrics; elongation; elastic recovery; artificial neural network; fuzzy logic
Introduction Elastic fabrics are an important way to achieve stretch comfort (freedom of movement) for body fitted with sports and outdoor wear. Elastic cloths used in athletics and sports may enhance the athlete’s performance in swimming, cycling, and so on. This type of fabric enables freedom of body movement by reducing the fabric resistance to body stretch. A simple body movement may enlarge the body skin by about 50% and the fabric must easily go with the stretch and recover on relaxation. Strenuous movements involved in active sports may require even better garment stretch. Drastic differences between skin and fabric movements result in limitations of movement to the wearer. Elastic fiber, yarn, and fabric provide the requisite elasticity to cloths (Voyce, Dafniotis, & Towlson, 2005). Fabrics containing elastane stretch fiber have a wide application value, especially because of their increased extensibility, elasticity, high degree of recovery, good dimensional stability, and simple care (Ceken, 1996; Mukhopadhyay, Sharma, & Mohanty, 2003; Tasmac, 2000). The clothing industry uses two types of basic pattern blocks, one for woven fabrics and the other for knitted fabrics. For woven fabrics, an extra amount (ease) is added which allows for a degree of body *Corresponding author. Email:
[email protected] Copyright Ó 2013 The Textile Institute
movement. The actual amount of recommended ease added varies between authors but is usually within the range of 4–6 cm per half pattern. In the case of knitted fabrics pattern blocks, the ease can be largely ignored as the inherent stretch properties of the fabrics allow for body movement. Many researches interest for dealing with the problems of designing for today’s stretch fabrics. They tried to establish a flexible and economical system for designing well-fitting body contouring apparel with knitted elastomeric. The methods used consisted of pattern construction and how to produce a reduced pattern and this has been applied to a garment produced from knitted stretch fabric of known extension and recovery properties (I-Chin, Cassidy, Cassidy, & Shen, 2002; Ziegert & Keil, 1988). Several criteria of the product design are given as follows: (1) satisfying the target values of the functional properties of knit stretch fabrics; (2) optimizing the final structure of fabrics; and (3) minimizing the quantity and the cost of raw materials. In the literature, some studies aimed to conceive new plating devices or to design new plated fabrics (Baozhu & Weiyuan, 2007; Bruer, Powell, & Smith, 2005; Doyle, 1953; Munden, 1959; Pusch, Wünsch, & Offermann, 2000). Cuden, Srdjak, and Pelko (2000)
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focused on the measurement of plated fabric properties such as elasticity and shrinkage before and after laundering, but did not investigate the effect of elastane ratio on these characteristics. Some researches (Gorjanc & Bukosek, 2008; Özdil, 2008) concerned only weaved fabrics made with lycra core-spun weft yarns. Other works (Ben Abdessalem, Ben Abdelkader, Mokhtar, & Elmarzougui, 2009; Ceken, 1996; Chemani & Halfaoui, 2006; Marmarali, 2003; Marmarali & Özdil, 2006; Miller, Atkins, & Rummel, 2006; Pfangen, 2003; Singh, 1974; Tasmac, 2000) have studied the effect of some single factors on comfort stretch properties. These properties are influenced by the finishing treatment, the amount of elastane, yarn count, yarn twist, yarn composition, fabric’s structure, and the operating parameters (gauge, loop length, etc.). They have not considered the combinational effects of several factors. Without considering the complex interactions of the various factors at the different processing stages, the weight of each factor and their synergistic effect on extension and recovery properties cannot be fully understood. When studying the effect of each structural parameter on the functional properties selected from the final product specifications, it is quite difficult to produce a large number of samples. In practice, the amount of learning samples is strongly constrained by the production or experiment costs. Accordingly, it is necessary to set up a model to solve it. It is the aim of our study. We try to develop a design support system for product designers using fuzzy logic and neural networks. By the support developed, we predict elongation, growth, and recovery test results of knits stretch fabric for course and wale direction. In order to reduce the model complexity, an original fuzzy logic-based
sensitivity variation criterion was developed to select the most relevant input variables and small-scaled artificial neural network (ANN) models have been set up with specific architectures adapted to the product diversity before the modeling procedure. Based on these models, designers, industrial, and researchers can optimize the comfort stretch of knit product according to the specifications, also permit to reduce machines adjustment duration. Experimental procedure Sample production Twenty different knit fabrics were used to select the most relevant input parameters. Table 1 shows the maximum, minimum, average, and standard deviation of knit fabric features used under study. The numeric values 0 and 1 were used to encode the corresponding knit feature and yarn composition (given in brackets). The greige fabrics were partially finished before evaluating their properties. The finishing conditions were chosen according to industrial tests adapted to elastane ratio of 5%. Fabric testing First, we note that the fabrics samples were conditioned in the testing laboratory under standard atmospheric conditions of 20 ± 2°C and 65 ± 2% relative humidity after a minimum period of 24 h conditioning in an NF ISO17025 certified laboratory. In this study, the tests carried out were concerning the determination of these parameters according to the French national organization for standardization (French Association of Normalization [AFNOR]). The evaluations of elastic properties (outputs) are executed according the AFNOR standard (NF EN 14704-1, 2005) with a cyclic loading standard test by using a constant speed gradient dynamometer
Table 1. The maximum, minimum, average, and standard deviation of knit fabric features used to select the most relevant input parameters. Inputs parameters Knitted structures Yarn composition Yarn count (Nm) Loop length (cm) Yarn twist (aNm ) Gauge Machine diameter (inch) Lycra proportion (%) Lycra yarn count (dtex) Lycra consumption (cm) Lycra tension (cN) Weight per unit area (g/m2) Thickness (m)
Mean value
Standard deviation
Maximum value
Minimum value
– – 50,000 0.327 110,000 23,770 31,000 3500 8070 0.207 4000 200,000 0.00086
– – 10,000 0.0822 10,000 4213 2000 1122 14,665 0.0322 0.800 31,000 0.00029
1 (rib1&1) 1 (100% viscose) 60 0.74 120 28 32 5 44 0.36 7 250 0.00105
0 (jersey) 0 (100% coton) 40 0.25 90 24 30 2 22 0.101 2 140 0.00065
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Figure 1. Fabric cyclic loading diagram.
LRX 2.5 K (Lloyd, UK) (500 mm min1). The fabric sample (50 300 mm) is grabbed with two roll clamps. Specimen loading starts by gradually increasing the load to 15 N and then decreasing the load until load zero. Loading was performed till the inelastic zone (15 N) in order to examine fabric recovery. Samples are tested in wale and course directions and cyclic loading curves are reported in Figure 1 (it was repeated five times). Three performance criteria of the fabric were investigated in this study, elongation, residual extension, and elastic recovery. Elongation can be explained as the changing of the form of material temporarily with the effects of out forces (pull etc.). This deformation recovers when the effect of out forces disappear. Residual extension is the permanent deformation amount of material with the effect of the force applied to it over a definite time. Recovery can be explained as the ratio between the original dimension and the permanent deformation. Cyclic loading test is a dynamic test that simulates deformation applied on fabric during wearing. After elongation, knitted fabric does not recover initial dimension. It can be explained by the hysteresis
phenomenon of spun yarns (Figure 1), yarn composition and structure, knitted fabric structure and properties, etc. Some related pictures of tested fabrics before cyclic loading test (a) and after cyclic loading test (b) in wale and course direction are illustrated in Figure 2. Modeling with ANNs In this section, we use ANNs for modeling the relationship between the structural parameters and the elastics properties of knitting fabrics. Different technologies are used to manufacture knitting fabrics. In this case, the structure of materials varies with applied technology and the corresponding knitting fabrics are then classified into a number of families each corresponding to one type of structure. Consequently, all the operating parameters and characteristics of yarn and fabric are divided into two groups. One group contains public parameters available for all the families of knits and the other group contains special parameters existing for each specific family. Therefore, two ANN models are developed. The general model (Figure 3(a)) takes into account the public parameters as inputs. This model can be used by all the families
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Figure 2. Appearance of some tested knitted fabrics.
Figure 3. General model including only public structural parameters: (a) special model including public and special structural parameters (b).
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of knits. For each family, a special model was established (Figure 3(b)). It takes into account both the public and the special parameters as inputs. In order to solve the problems related to the lack of available learning data or samples, small-scaled ANN models are built (Huang & Moraga, 2004; Raudys & Jain, 1991; Vroman, Koehl, Zeng, & Chen, 2008; Yuan & Fine, 1998). The Levenberg–Maquardt learning procedure, based on a backpropagation algorithm, is used for calculating the unknown parameters of the general model from the public learning data-sets. In the special model, the weights connecting the public inputs to the hidden neurons (HN) are kept invariable. Merely, the weights connecting the special input neurons to the HN are calculated during the learning phase using the error backpropagation algorithm.
Variable selection and data preprocessing for neural network models The fuzzy logic based sensitivity variation criterion developed by Deng, Vroman, Zeng, and Koehl (2007) was used to select the most relevant structural variable. The important benefit of this technique is that it can deal with a small number of learning data-set. Its principle consists to calculate Euclidean distances or sensitivity variation of each input variable related to the output variable. The sensitivity variation for all inputs is defined according to the two following principles: (1) If a small variation of an input variable Dx corresponds to a large variation of the output variable Dy; then this input variable has a great sensitivity value S. (2) If a large variation of an input variable Dx corresponds to a small variation of the output variable Dy; then this input variable has a small sensitivity value S: Based on these principles, a fuzzy model is built taking into account the input data variation Dx and the output data variation Dy as two input variables and the sensitivity S as output variable (Deng et al., 2007). To simplify the selection procedure, we developed an original method using fuzzy C-means (FCM) (Bezdek, 1981), based on this fuzzy sensitivity variation criterion, to classify sensitivity variation values into classes depending on the application. Inputs constituting the smallest class are eliminated; the rest (list CE) is used for the selection algorithm in the next section.
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Inputs: process input variables X ¼ fx1 ; . . . ; xk ; . . . ; xm g, and one related specific output yl . Output: relevant process parameters Xr and related sensitivity variation value DScorr(xp ; xk ) denotes correlation between xp and xk (1) Calculate the sensitivity variation of inputs in X related to yl denoted DSl ¼ fDS1;l ; :::; DSk;l ; :::; DSsize(X );l g, (2) Classify DSl into FCM classes; eliminate inputs that constitute the smallest class, (3) For each pair of relevant inputs (xk ; xp ), calculate the linear correlation coefficient, (4) If DSk;l 2 CE; and maxk–p jcorr (xk ; xp )j\a (correlation threshold). Then xk is considered relevant to y1 : (5) If DSk;l and DSp;l 2 CE; jcorr (xk ; xp )j a and DSk;l > DSp;l . Then xk is considered relevant to y1 ; xp is correlate to xk and should be eliminated. (6) Xr ¼ CEnfxp g: The α value is defined by the experts. Over α is small, less variables in the final list are correlated. When this procedure is completed, we could obtain a significant and independent list of the most relevant parameters related to specific output yl . Model design and network training Having choosing appropriate input variables, the following steps build the models according to selected parameters. The data in neural networks are categorized into two sets: training or learning sets and test or overfitting test sets. The learning set is used to determine the adjusted weights and biases of a network. The test set is used for calibration, which prevents overtraining networks. The overfitting test set should consist of a representative data-set. It should be approximately 10–40% of the size of the training set of data. The sigmoid function is used (Larose, 2005; Oussar, Monari, & Dreyfus, 2004). The overall function represented by the network type is: ! Hid n X X y ¼ f (x) ¼ Sigm xij wij Vj vj h; (1) j¼1
i¼1
where x is a n-dimensional input vector, w is the weight vector connecting the input units with the single output neuron, and h is the output neuron’s bias value; Hid is the number of HN, v is the weight vector connecting the hidden layer with the output
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neuron, and V is the HN’ bias values. Sigm(x) is the common sigmoid transfer function: Sigm (x) ¼
1 : ½1 exp ( x)
(2)
The input to individual ANN nodes must be numeric and fall in the closed interval [0,1]. Because of this conversion method, the normalization technique was used in the proposed ANN according to the following formula:
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x0 ¼
xi min (x) ; max (x) min (x)
(3)
where xi is a feature instance and x represents the set of a feature type. Output values resulted from ANN were also in the range [0,1] and converted to its equivalent values based on reverse method of normalization technique. Selecting the optimal model architecture The fitted model is expected not merely to predict accurately the observed data-set but also to generate satisfactory predictions for unseen (test) data-set drawn from the same population as the observed (training) data. Such a model is able to generalize (extrapolate) well within the data-set range. The estimation of the best fit parameters based on the naïve minimization of a merit function based on the fidelity to the learning data-set alone can steer to a fitted model with very poor predictive aptitude. Given a sufficient number of parameters (degrees of freedom), the model can be fitted to pass through each observed data points perfectly. This strict interpolation is undesirable and must be avoided in practice since the observed data are unavoidably corrupted with measurement noise. This overfitting phenomenon can be avoided using the leave-one-out cross-validation criterion for estimation of optimal regularization parameters of the regularization networks (Rogier & Geatz, 2003). Obviously, traditional a multilayer perception networks are not equipped with any noise filtering capacity and the above procedure cannot be applied to such networks. Model selection was performed basically by estimating the generalization aptitude of the models trained as described, using the “leave-one-out score” Ep : sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n h i2 X R(k) Ep ¼ ; k k¼1
(4)
is the prediction error on the example k where R(k) k when the latter has been removed from the learning data-set and the model has been trained with the remaining examples. Since the computation of the leave-one-out score is computer-intensive, approximations of the leave-one-out errors R(k) were computed k by the “virtual leave-one-out” method, described in (Oussar et al., 2004). In this application, the model is based on « p » samples of knits fabrics. Training uses the leave-oneout technique. After training, the optimal model architecture was chosen by using a selection methodology (Alibi, Fayala, Jemni, & Zeng, 2012; Geman, Bienenstock, & Doursat, 1992; Golub & Van Loan, 1996; Monari & Dreyfus, 2000, 2002; Rogier & Geatz, 2003; Vapnik, 2000). Model evaluation and interpretation Performance measure In order to evaluate the performance of the obtained network models, three statistical performance criteria, including root-mean-square error (RMSE), coefficient of correlation (R), and mean absolute relative error (MARE), were used in this study. These parameters were calculated for training (tr) and testing (T) phases: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 uP u n t k¼1 ypk yk RMSE ¼ ; (5) n Pn k¼1
R2 ¼ P n
yk ypk
2
2 ; k k y y p p k¼1
k N 1X yk yp MARE ¼ ; N i¼1 ykp
(6)
(7)
where yk and ykp , respectively, the prediction of the output by the model and measured value of the process output for observation k: Model interpretation In spite of their many advantages such as universal function approximation, robustness, capability to take into account the nonlinear relationship of structural and functional parameters, and ability to learn from examples, one of the main limitations of ANN models is their “black-box” system approach which is unable to explain the weights of each inputs and their synergistic effect on outputs (Table 2).
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Table 2. Input and output parameters. Factors
Variable names
Processing parameters (input)
Knitted structures (x1), yarn composition (x2), yarn count (x3), loop length (x4), yarn twist (x5), gauge (x6), machine diameter (x7), lycra proportion (x8), lycra yarn count (x9), lycra consumption (x10), lycra tension (x11), weight per unit area (x12), and thickness (x13) Elastic recovery in wale direction (y1)
Properties (output)
Table 3. Selection of relevant (a) and independent (b) input variables related to elastic recovery in wale direction, using the fuzzy logic-based sensitivity variation criterion.
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(a) Inputs All inputs, x1 to x13 (b) Remaining inputs (list CE) x9, x13, x2, x1, x12, x8, x4, x6, x3, x5, x10
Significance ranked by ascending order DS
Most relevant inputs (list CE)
Irrelevant inputs
x9, x13, x2, x1, x12, x8, x4, x6, x3, x5, x10, x11, x7
x9, x13, x2, x1, x12, x8, x4, x6, x3, x5, x10
x11, x7
Correlate input (α = 0,8) x5, x10
Numerous methods have been proposed to conquer this shortcoming (Jayadeva, Guha, & Chattopadhyay, 2003). In this paper, the connection weight approach proposed by Olden and Jackson (2002) was used to calculate the importance of ANN input variables, as Olden, Joy, and Death (2004) found that this approach provided the best overall technique for accurately ranking ANN input relevancy in comparison to other commonly used techniques. This approach consists to calculate the product of the raw input-hidden and hidden-output weights between each input and output neuron. Next, it sums the products across all HN, which is defined as Si The relative contributions of ANN inputs in calculating the output are dependent on the scale and direction of the connecting weights. Input variable with bigger connection weights (higher Si ) is more relevant in the prediction process compared to the inputs with smaller connection weights (lower Si ). Negative and positive connection weights, respectively, decrease and increase the value of the predicted response. Results and discussion Fuzzy sensitivity variation for selecting relevant process parameters The fuzzy-based method presented in this paper was used for selecting the relevant input variables and removing irrelevant ones. We have chosen to present the selecting procedure, the results and discussions related to the elastic recovery in wale direction as an application example.
Significant and independent list of the most relevant inputs x9, x13, x2, x1, x12, x8, x4, x6, x3
According to our application, DSk;l values are classified into three classes (small, medium and large) using FCM algorithm. Table 3(a) represents the first step to classify the sensitivity variation of structural parameters related to elastic recovery in wale direction and then removing small class’s inputs. Table 3(b) shows the next step for identifying independent list of most relevant inputs. According to these tables, the relevant parameters selected from this criterion could be ranked in a significant order of relevancy: lycra yarn count (x9) > thickness (x13) > yarn composition (x2) > knitted structures (x1) > weight per unit area (x12) > lycra proportion (x8) > loop length (x4) > gauge (x6) > yarn count (x3). Therefore, by using the fuzzy sensitivity variation criterion, the number of structural parameters was reduced from 13 to 9. Therefore, it can be concluded that the fuzzy sensitivity variation criterion could efficiently filter data complexity related to elastic recovery and provide merely an enhanced ranking result according to the process variables relevancy. This permitted a good comprehension on the structural variable since the adjustable variables are more concise and easier to be interpreted physically. The selected parameters were used to build the ANN models. Optimum neural networks architecture The focus of this research was constrained to pure cotton, pure viscose, viscose/lycra, and cotton/lycra plated knitted constructions. We produced a series of 340 knitted fabrics commonly used in the clothing industry
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Table 4. Statistical values of input (a) and outputs (b) parameters of training and test set fabrics.
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Mean value (a) Inputs parameters Knitted structures Yarn composition Yarn count Gauge Lycra proportion (%) Lycra yarn count (dtex) Weight per unit area (g/m2) Thickness (m) Interlock loop length (cm) Jersey loop length (cm) 1&1 rib loop length (cm) 2&2 rib loop length (cm) (b) Outputs parameters Output 1: elongation in wale direction (%) Output 2: elastic recovery in wale direction (%) Output 3: residual extension in wale direction (%) Output 4: elongation in course direction (%) Output 5: elastic recovery in course direction (%) Output 6: residual extension in course direction (%)
Standard deviation
Train
Test
Train
– – 49.138 23.770 1.123 8.070 220.679
– – 50.28 24.17 0.93 6.19 209.09
2.775 0.303 10.163 4.213 2.122 14.665 64.351
0.00078 1.43 0.327 0.6125 0.675
0.00076 1.03 0.267 0.565 0.486
0.00021 0.287 0.0822 0.0699 0.0876
Test 2.75 0.24 10.64 3.99 1.98 12.88 61.56 0.00022 0.256 0.0745 0.0621 0.0569
Maximum value Train 9 2 80 28 10 44 548 0.00153 2.42 0.74 0.83 0.87
Test 9 2 80 28 8 44 422 0.0016 2.72 0.68 0.92 0.79
Minimum value Train 1 1 20 16 0 0 120 0.00044 1.08 0.25 0.37 0.62
Test 1 1 20 14 0 0 119 0.00044 0.95 0.25 0.32 0.58
30.85
25.61
24.97
16.78
139.24
106.44
12.68
10.13
77.34
75.92
8.07
7.95
96.16
91.54
55.55
52.83
5.77
5.51
2.43
2.45
17.25
14.75
1.5
91.96
82.44
57.51
34.53
563.99
167.00
13.26
28.12
67.65
65.84
14.20
14.19
91.5
91.79
30.49
28.60
30.65
30.56
24.14
21.74
159.5
by using different industrial circular knitting machines (single jersey, double jersey, interlock; tubular and large diameter; diameter = 16–34 inch, gauge = 18–28). Ground yarn was a 100% combed cotton (1) and 100% viscose yarn (2) (Nm = 28–80) and plating yarn was a lycra monofilament (22, 33, and 44 dtex) plated at half feeder. The fabric samples were comprised of nine different knitted structures, single jersey (1), single lacoste (2), double lacoste (3), polo pique (4), visible molleton (5) invisible molleton (6), 1/1 rib (7), 2/2 rib (8), and interlock (9). The 340 measurements were randomly divided into a training database of 244 values for training and model selection, and a test database of 96 values for the final assessment of the generalization performance of the model. Table 4 presents the statistical values of selected input and output parameters of training and test set fabrics. The network architecture used a three-layered feed-forward network with sigmoid hidden-unit activity and a single linear output unit. There are six knitting fabrics families different in the formation (simple or complex structure) and the knitting technologies (simple and double needle machine or interlock machine).
109.5
2
2
3.25
A general model is built using a neural network for all the knitting samples. It characterizes the relationship between the selected structural parameters and the corresponding functional property. For the functional properties, using the fuzzy logic-based sensitivity variation criterion, we take the eight most relevant structural parameters as public input variables. A special model is built for the family of knitting materials produced using a specific knitting technology (Exp: interlock machine). Its architecture and parameters are built based on the corresponding general model. For example, the interlock loop length is added to the set of the input variables of the general model to build the special model corresponding to interlock knitting family. Figure 4 shows the special model built for predicting the functional properties with eight public parameters (knitted structures, cotton yarns counts, gauge, lycra proportion, lycra yarn count, lycra consumption, weight per unit area, and thickness) as input variables. The special structural parameter is then added to the set of these eight input variables. The architecture and parameters of specific model are built based on the corresponding general model. Only the weights connecting the specific input neurons to HN are added. Therefore, this model
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Figure 4. Special model for the interlock knitting family.
benefits from both the specificity of each stretch knitted fabrics class and the generality of all these classes. Consequently, we need to build these two types of models to solve the problems related to the lack of available learning samples. The goal of ANN design is to find a model for which the estimate of the root-mean-square generalization error is on the order of the standard deviation of the noise present in the training data (Geman et al., 1992). To that effect, models of increasing complexity (i.e. increasing number of HN) were trained, and the virtual leave-one-out score Ep of each model was computed. The root-mean-square error on the training set (RMSEtr ) was also computed; those quantities are reported in Table 5. As expected, Ep decreases when the number of HN increases and starts increasing when the number of parameters is big enough for overfitting to arise. On the other hand, RMSEtr on the training data-set decreases when the number of HN increases (Table 5). Moreover, the learning task enhanced when the number of HN exceeds the eight,
but the generalization ability degraded. In fact, the generalization error decreases and the overfitting phenomenon starts. These results can be explained by the fact that ANN architecture with small number of HN is unable to extract the nonlinearity between the inputs and outputs. Whereas, a model with too many HN can perfectly adjust the training examples and the model dedicated a large part of its degrees of freedom to learn these examples. Therefore, it fit the noise that exists in the data, hence generalizes poorly. As a result, the predictions will be deprived of significance because its performance will depend for the largest part on the particular training data-set. Accordingly, the selected model should guarantee the optimum trade-off between learning aptitude and generalization ability. For our case, the generalization error Ep does not increase significantly when the number of HN exceeds the eight, in the investigated range. In order to minimize the number of parameters, eight HN were
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Table 5. Optimization of the number of HN for the neural networks: wale direction (a) and course direction (b). Output 1: elongation in wale direction RMSEtr
Output 2: elastic recovery in wale direction
Output 3: residual extension in wale direction
q
Ep
RMSEtr
q
Ep
RMSEtr
q
Ep
11 21 31 41 51 61 71 81 91 101
26.883 29.652 11.246 16.519 11.075 11.616 10.503 10.801 10.906 12.071
5.017 4.656 4.235 3.873 3.466 3.502 2.84 2.689 2.329 2.277
11 21 31 41 51 61 71 81 91 101
7.231 5.217 5.094 5.034 5.704 6.19 5.674 5.796 5.897 6.631
1.794 1.534 1.366 1.168 1.037 0.895 0.888 0.714 0.68 0.556
11 21 31 41 51 61 71 81 91 101
1.937 1.756 1.706 1.701 1.602 1.509 1.726 1.307 1.955 1.703
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(a) Number of HN 1 2 3 4 5 6 7 8 9 10
32.85 25.215 6.48 5.891 6.237 4.969 4.056 2.966 2.525 1.461
(b) Number of HN Output 4: elongation in course direction
1 2 3 4 5 6 7 8 9 10
Output 5: elastic recovery in course direction
Output 6: residual extension in course direction
RMSEtr
q
Ep
RMSEtr
q
Ep
RMSEtr
q
Ep
35.266 27.674 23.018 18.281 15.778 14.126 12.926 4.405 6.342 5.861
11 21 31 41 51 61 71 81 91 101
50.124 41.478 40.99 35.23 31.781 24.639 27.52 9.79 22.076 31.082
7.23 6.274 5.729 5.343 4.541 4.465 4.153 3.725 3.576 3.22
11 21 31 41 51 61 71 81 91 101
7.55 7.138 6.959 7.443 7.757 7.242 18.064 7.752 38.57 17.637
46.121 9.963 9.183 7.33 7.907 7.284 6.249 5.445 5.205 4.967
11 21 31 41 51 61 71 81 91 101
26.299 13.318 12.828 14.457 12.625 14.028 15.06 11.526 13.611 18.464
selected. The final optimized architectures of neural network are shown in Figure 4, corresponding to 81 parameters. To test the generalization performance of the optimal trained network, validating processes was applied using the test database (Table 4). The main quality indicator of a neural network is its generalization ability, its ability to predict accurately the output of unseen data. The experimental vs. predicted values of test data-set are shown in Figure 5, as it can be observed, the predictability of ANN fits very well. RMSET and R2T for the feed-forward neural network were computed. Computations were performed for all outputs (Table 6). Neural networks provide quite satisfactory predictions for all functional properties from a global point of view: R2T is larger than 0.9 while RMSET is lower than 3.5. Mean absolute relative errors MARET were used to evaluate the performance of the proposed ANN in prediction technique. These levels of error (mean 6%) are satisfactory and smaller than errors that normally arise due to experimental variation and instrumentation accuracy.
Prediction assessment of the product functional properties Table 7 gives the details of the experimental results on the functional properties and the corresponding predicted results obtained from the general models and the special models. Figure 6 compares the predicted values of these functional properties obtained from the general and the special models and the real physical measures, respectively. The results demonstrated good agreement between the experimental and predicted values from special models (R2tr > 0.9). From these outcomes, it should be noted that the special models give lower prediction errors (averaged error: 6%) than the general models (averaged error: 12%). This observation can be explained as follows: • The general model uses samples from numerous families which differ from each other in many aspects while the special model merely uses samples from the same family. The general
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Figure 5. Experimental vs. predicted values for studied properties: data-set validation.
Table 6. Results of testing and validating neural network models for all comfort-stretch properties. Outputs Output Output Output Output Output Output
1: 2: 3: 4: 5: 6:
elongation in wale direction elastic recovery in wale direction residual extension in wale direction elongation in course direction elastic recovery in course direction residual extension in course direction
RMSET
MARET (%)
R2T
2.2 3 0.5 3.16 3.5 3.8
6 7 3 7 4 9
0.983 0.87 0.956 0.936 0.937 0.95
Table 7. Experimental results on the comfort-stretch properties for all product families. General model Outputs Output Output Output Output Output Output
1: 2: 3: 4: 5: 6:
Special model
Avg. error (%)
SD (%)
R2tr
Avg. error (%)
SD (%)
R2tr
8 3 14 17 6 23
13 3 13 18 6 24
0.912 0.81 0.842 0.924 0.865 0.867
4 2 9 7 4 6
5 3 10 5 4 7
0.995 0.91 0.915 0.971 0.93 0.944
elongation in wale direction (%) elastic recovery in wale direction (%) residual extension in wale direction (%) elongation in course direction (%) elastic recovery in course direction (%) residual extension in course direction (%)
model cannot benefit from the specificity of each stretch knitted fabrics family. • The special model is set up based on the corresponding structure of the general model. Merely,
the weights connecting the specific input to HN are added. Thus, it takes into account both the specificity of each stretch knitted fabrics family and the generality of all families.
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Figure 6. Comparison between general and special models, related to comfort stretch properties in course and wale direction: residual extension (a,b), elastic recovery (c,d), and elongation (e,f).
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Typical plots of the experimental vs. predicted values of selected stretch knitted fabrics are shown in Figures 7–9 and the results are discussed as following: for some materials (i.e. cotton and viscose), the predicted values of elastic recovery in course direction closely matched to experimental values (Figure 7(b)), showing the ANN model capability, whatever the type of raw materials and the available amount of data. Though, whatever the knitted structure’s the ANN model fits very well, solving the lack of available data-set of some knitted structures due to production constraints (Figure 7(a)). As well, the model accurately predicted the desired elastic recovery in course direction at high and lower values. Moreover, the model was able to predict elastic recovery in course direction whatever the gauge (Figure 8(b)). The developed ANN model is expected to be used for several circular knitting machines.
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Results show also the robustness with good accuracy of the special models for extreme value of yarn count (Figure 8(a)), lycra proportion (Figure 9(a)), and lycra yarn count (Figure 9(b)). It should be noted that this modeling procedure has proved its ability to process the existing constraints in others techniques, such as the nonlinearity in statistic techniques and initial and boundary conditions in numerical simulations (Hasan, Sulaiman, & Othman, 2011; Layeghi, Karimi, & Seyf, 2010). The developed ANN models are expected to help engineer to decide about designing new stretch knitted fabrics before the actual manufacturing by taking into account, mainly, the operating parameters, large types of knitted structures, and elastane properties. As well, using operating parameters as inputs of ANN model to predict comfort, stretch properties of fabrics were not investigated before.
Figure 7. Experimental and neural network predict values of elastic recovery in course direction for: knitted structures (a) and yarn composition (b).
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Figure 8. Experimental and neural network predict values of elastic recovery in course direction for: yarn count (a) and gauge (b).
Prediction interpretation Table 8 gives the connection weights between the input and hidden layers and the connection weights between the hidden and output layers of the selected ANN model. These weights could be utilized for interpretation of the physical effect of inputs on outputs. To compare, the ranking of inputs as per relative importance obtained from the fuzzy sensitivity variation criterion and the connection weights technique, we use the same output (elastic recovery in wale direction). The relative importance of the input variables as determined following the connection weight technique (Olden et al., 2004) is presented in Table 9. Results showed that lycra yarn count was the most important parameter for elastic recovery in wale direction (Si value 14.9095) followed by thickness (Si value
12.591). Moreover, it could be noticed that the ranking of inputs as per relative importance for elastic recovery in wale direction was the same result obtained from the fuzzy sensitivity variation criterion. This finding confirmed that the selected parameters had an influence on the elastic recovery. However, it could be shown that weight per unit area and knitted structures had a negative influence on the prediction of the output. This result indicated that elastic recovery values decreased with increase in weight per unit area and knitted structures values. Conversely, lycra yarn count, lycra proportion, thickness, loop length, yarn composition, gauge and yarn count had a positive influence on the prediction of the output. The increasing of ground yarn count resulted in improved elastic recovery. In fact, we can introduce more elastane fiber on stitch formed by a thinner
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Figure 9. Experimental and neural network predict values of elastic recovery in course direction for: lycra proportion (a) and lycra yarn count (b).
Table 8. Values of weights between the input (a), output (b) layer and the hidden layer of the ANN.
(a) Input Knitted structures Yarn composition Yarn count Gauge Lycra proportion (%) Lycra yarn count (dtex) Weight per unit area (g/m2) Thickness (m) Loop length (cm) (b) Output Elastic recovery in wale direction (%)
HN1
HN2
HN3
HN4
HN5
HN6
HN7
HN8
4.34 0.97 0.76 4.02 0.76 1.13 4.75 6.2 1.05
1.84 0.72 2.85 4.04 2.98 0.98 10.04 5.91 0.86
1.07 0.47 0.86 1.2 0.26 0.5 1.27 2.14 0.3
4.49 1.27 1.5 6.27 2.22 3.17 11.03 2.55 3.93
4.42 0.51 1.91 6.18 4.37 1.18 6.09 3.3 0.88
1.14 1.03 1.89 1.47 3.92 3.36 2.95 2.15 2.21
0.7 1.73 0.06 0.05 0.55 0.49 1.62 0.1 0.37
4.85 0.35 1.13 2.36 0.03 7.7 4.48 7.3 1.2
1.8
1.27
2.92
1.08
1.46
2.21
2.67
1.11
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Table 9. Relative importance of different inputs as per connection weight approach for prediction of elastic recovery in wale direction by the ANN. Output Elastic recovery in wale direction (%) Output
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Knitted structures Yarn composition Yarn count Gauge Lycra proportion (%) Lycra yarn count (dtex) Weight per unit area (g/m2) Thickness (m) Loop length (cm)
Si value as per connection weight approach
Ranking of inputs as per relative importance
6,4712 7,1961 0.8301 0.9298 4,4584 14,9095 5,0581 12,591 4,1662
4 3 9 8 6 1 5 2 7
ground yarn. In the same way, the increasing rate of elastane causes freedom of stitch and they will not be more locked because the elastane yarn is less tight. This results in a decrease of stitches density thus reducing weight per unit area. The elastic recovery values increased with increase in lycra yarn count and lycra proportion values; this is due to the increase of potential energy inside fabric that allows the improved recovery levels of fabric dimensions. This finding also indicated that viscose knit fabrics achieved better recovery than cotton fabrics. This result can be explained by the fact that viscose fiber has greater elasticity than cotton. The larger partial recovery of the cotton knitted fabric is due to hysteresis phenomenon of cotton spun yarns having more plastic deformation behavior related to the slippage and viscoelasticity of cotton fiber. The residual deformation obtained after cyclic loading test can be explained by plastic deformation due to fiber residual extension and/or fiber slippage because elastane yarn is purely elastic. Fiber residual extension depends on the fiber viscoelasticity, while fiber slippage phenomenon depends on torsion and bending of the yarn. In addition, it indicated that by considering fabric made of the same fiber type, the elastic recovery of simple structure fabrics was better than more complex fabrics. An open knit fabric offers higher stretch than a close knit structure; the stitches will not be more locked. These results were consistent with previous works (Ben Abdessalem et al., 2009; Mukhopadhyay et al., 2003; Singh, 1974). As a result, the outcomes obtained from ANN models could be used to validate physical knowledge on the relationship between structural parameters and comfort stretch properties. Hence, a conclusion can be draw that the developed ANN models could explain the physical effect of inputs on the outputs.
Conclusions In this study, a support system was built up for optimizing the design of knit stretch fabrics, in agreement with the specifications. The relationship between the structural parameters and fabrics features of knit stretch products is established using ANN. In order to reduce the complexity of the ANN models and solve the lack of available data-set, also deal with the risk of losing some relevant variable, an original selection procedure was proposed using FCM algorithm to select the most relevant structural parameters. The selection procedure of structural parameters allows fabric designers to focus on the most relevant parameters in order to conduct actual manufacturing of the new knit stretch product. According to this approach, it was found that lycra yarn count, thickness, yarn composition, knitted structures, weight per unit area, lycra proportion, loop length, gauge, and yarn count were important parameters. This shows that the effects on comfort stretch properties depend not only on knitting parameters but also on fabric features. In the modeling procedure, two types of models are set up. A general model is firstly developed for all families of knit stretch products. It is built from the data-set of public inputs. A special model is then built for each family of knit stretch products by adding special structural parameters to the data-set of public inputs. The leave-one-out approach has been used to test the efficiency of the general and special model. The developed ANN models were different in training algorithms. The neural network optimization method had enhanced the model accuracy. Results show low prediction errors of special models compared to general models. The simulation of these models allows designers to optimize structure of materials more systematically, substituting the traditional hit-and-trial approach and hence reduce testing time and cost.
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The relative importance of the input parameters was established via the connection weight approach. The outcomes were found to agree with those calculated via the fuzzy logic-based sensitivity criterion. Therefore, it is believed that ANN models could efficiently be applied to the knitting industry to understand, evaluate, and predict comfort stretch taking into account knitting parameters and fabric features as inputs.
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